A Statistical Model of Aggregates Fragmentation

A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are formulated on a lattice and mimic two important features of the process -- a crack moves against the stress gradient and its energy depletes as it grows. We perform numerical simulations of the model for two-dimensional lattice and reveal that the mass distribution for small and intermediate-size fragments obeys a power-law, F(m)\propto m^(-3/2), in agreement with experimental observations. We develop an analytical theory which explains the detected power-law and demonstrate that the overall fragment mass distribution in our model agrees qualitatively with that, observed in experiments.